Final answer:
The conclusion that Alex has set a new personal record for running a mile is true.
Step-by-step explanation:
The given statement is:
If Alex runs a mile in under 6 minutes, then he will have a new personal record.
Given: Alex ran a mile in 5 minutes and 57 seconds.
Conclusion: Alex has set a new personal record for running a mile.
To determine if the conclusion is true or false, we need to verify if the condition in the given statement is satisfied. The condition states that if Alex runs a mile in under 6 minutes, then he will have a new personal record.
Since Alex ran a mile in 5 minutes and 57 seconds, which is less than 6 minutes, the condition is satisfied. Therefore, the conclusion is true. Alex has indeed set a new personal record for running a mile.
So, the correct answer is a) True.